652 research outputs found
GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring
Compressive sensing promises to enable bandwidth-efficient on-board
compression of astronomical data by lifting the encoding complexity from the
source to the receiver. The signal is recovered off-line, exploiting GPUs
parallel computation capabilities to speedup the reconstruction process.
However, inherent GPU hardware constraints limit the size of the recoverable
signal and the speedup practically achievable. In this work, we design parallel
algorithms that exploit the properties of circulant matrices for efficient
GPU-accelerated sparse signals recovery. Our approach reduces the memory
requirements, allowing us to recover very large signals with limited memory. In
addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc
parallelization of matrix-vector multiplications and matrix inversions.
Finally, we practically demonstrate our algorithms in a typical application of
circulant matrices: deblurring a sparse astronomical image in the compressed
domain
Scalable iterative methods for sampling from massive Gaussian random vectors
Sampling from Gaussian Markov random fields (GMRFs), that is multivariate
Gaussian ran- dom vectors that are parameterised by the inverse of their
covariance matrix, is a fundamental problem in computational statistics. In
this paper, we show how we can exploit arbitrarily accu- rate approximations to
a GMRF to speed up Krylov subspace sampling methods. We also show that these
methods can be used when computing the normalising constant of a large
multivariate Gaussian distribution, which is needed for both any
likelihood-based inference method. The method we derive is also applicable to
other structured Gaussian random vectors and, in particu- lar, we show that
when the precision matrix is a perturbation of a (block) circulant matrix, it
is still possible to derive O(n log n) sampling schemes.Comment: 17 Pages, 4 Figure
Computation- and Space-Efficient Implementation of SSA
The computational complexity of different steps of the basic SSA is
discussed. It is shown that the use of the general-purpose "blackbox" routines
(e.g. found in packages like LAPACK) leads to huge waste of time resources
since the special Hankel structure of the trajectory matrix is not taken into
account. We outline several state-of-the-art algorithms (for example,
Lanczos-based truncated SVD) which can be modified to exploit the structure of
the trajectory matrix. The key components here are hankel matrix-vector
multiplication and hankelization operator. We show that both can be computed
efficiently by the means of Fast Fourier Transform. The use of these methods
yields the reduction of the worst-case computational complexity from O(N^3) to
O(k N log(N)), where N is series length and k is the number of eigentriples
desired.Comment: 27 pages, 8 figure
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